Let \(D\) be a strongly connected digraph with order at least two. Let \(M(D)\) denote the middle digraph of \(D\), and let \(\kappa(D)\) and \(\lambda(D)\) denote the connectivity and arc-connectivity of \(D\), respectively. In this paper, we study super-arc-connected and super-connected middle digraphs and the spectrum of middle digraphs.